One-shot computation of reachable sets for differential games

Abstract

We present a numerical method for computing backward reachable sets in differential games. A backward reachable set for time t is captured by the t sublevel set of the lower value function of the game, which coincides with the viscosity solution of a stationary Hamilton-Jacobi-Isaacs (HJI) equation. We solve the stationary HJI equation in a computationally efficient way that does not involve any numerical integration over time, which would otherwise be required for time-dependent HJI equations. Backward reachable sets for all time points can simultaneously be extracted from the solution. The performance of the method is demonstrated by investigating the growth of multicellular structures of non-malignant and malignant breast cells as a proof of principle. Copyright © 2013 ACM.